#with(queue):

#this is a fixed version of the line_vertices in everything.txt
#(see comment in everthing.txt for usage)
#this one allows teh start and end vertices to be boundary points

our_line_vertices:=proc(m_func,startpt,first_neighbor,rest_neighbor)
 local lineT,vm,outlist,ending,last_pt;

 lineT:=gasket(m_func);
 vm:=vertices(m_func);
 make_neighbors(lineT,m_func,vm);

 outlist:=[startpt,lineT[startpt,first_neighbor]];

 ending:=last_digits(lineT[startpt,first_neighbor]);
 last_pt:=lineT[startpt,first_neighbor];

 while nops(lineT[last_pt,rest_neighbor])>1 and last_digits(lineT[last_pt,rest_neighbor])=ending do
    outlist:=[op(outlist),lineT[last_pt,rest_neighbor]];
    last_pt:=lineT[last_pt,rest_neighbor];
 od;

 outlist:=[op(outlist),lineT[last_pt,rest_neighbor]];

 outlist;
 end;

#returns the number of steps in the lvlth gasket between startv
#and endv...ie the graph distance.
#this uses a bredth first search

verDist:=proc(lvl,startv,endv)
	local T,ver,vertex,Q,val,i,numneighbors;
	ver:=ourVertices(lvl);
	T:=gasket(lvl);
	make_neighbors(T,lvl,ver);
	for vertex in ver do
		T[vertex,5]:=false;
	end do;
	Q:=queue[new]();
	queue[enqueue](Q,[startv,0]);
	while not queue[empty](Q) do
		val:=queue[dequeue](Q);
		if val[1]=endv then
			return(val[2]);
		end if;
		if nops(val[1])<2 then
			numneighbors:=2;
		else
			numneighbors:=4;
		end if;
		for i from 1 to numneighbors do
			if not T[T[val[1],i],5] then
				queue[enqueue](Q,[T[val[1],i],val[2]+1]);
				T[T[val[1],i],5]:=true;
			end if;
		end do;
	end do;
	return(-1);
end;


#this is an optimzation of gasket in everything.txt
#it sets T[i,-1] to be vertices(i) for i from 1 to m
#this cuts down on calls to vertices in functions that
#assume this call to verGasket

verGasket:=proc(m)
     local i, vm, T;

     vm:= vertices(m);
     T:=table();
     for i from 1 to nops(vm) do
         T[vm[i], 0] := vm[i]    od;

     for i from 1 to m do
	T[i,-1]:=ourVertices(i);
     end do;


    return(T);
 end;

#firstP:=proc(nums,len)
#	local l;
#	l:=[];
#	for i from 1 to len do
#		l:=[op(l),nums[1]];
#	end do;
#	return(l);
#end;

#nextP:=proc(nums,lastp)
#	local newp,lastnum;
#	lastnum:=nums[nops(nums)];
#	
#end;